Variance Estimation Using List Sequential Scheme 'for' Unequal Probability Sampling

Yves G. Berger

Abstract:
The problem of variance estimation is discussed in the light of the list sequential scheme proposed by Chao (1982), in which units are selected without replacement and with unequal probabilities. The variance is hard to estimate as it requires a large number of second-order inclusion probabilities. We prove that it is unnecessary to compute all these probabilities. We show that variance estimation needs only N numbers, where N is the population size.

Keywords:
Variance estimation; sampling without replacement; Horvitz-Thompson estimator; Yates-Grundy estimator; inclusion probabilities; probability proportional-to-size sampling.